I used to have one of these. They called them "Rollup Keyboards". You can probably still find a few online. They are water-resistant/proof and you're supposed to be able to roll them up and take them wherever, however they weren't designed very well and over a short amount of time the internal connections become loose and will no longer work correctly.

I didnt recognize these from the first picture.
These keyboards are sold for less than 10-15$ all around (here in Germany there are shops like saturn and media markt selling these).

They are not meant to be opened at all, also they are not meant to last more than a few times folding or rolling them.
Also they are very bad for your fingers. It is like wearing a broken shoe, in which you have to spread your toes to not loose your shoe.